Prediction of Material Strength and Fracture. Hydrodynamics Code

Transcription

1 LA UC-7 and UC- Issued: August 1994 Prediction of Material Strength and Fracture of Glass Using the SPHINX Smooth Particle Hydrodynamics Code David A Mandell Charles A Wingate N A T I O N A L L A B O R A T O R Y Los Alamos, New Mexico I

2 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof

3 DISCLAIMER Portions of this document may be illegible in electronic image products Images are produced from the best available original document

4 PREDICTION OF MATERIAL STRENGTH AND FRACTURE OF GLASS USING THE SPHINX SMOOTH PARTICLE HYDRODYNAMICS CODE David A Mandell and Charles A Wingate ABSTRACT The design of many military devices involves numerical predictions of the material strength and fracture of brittle materials The materials of interest include ceramics, that are used in armor packages; glass that is used in truck and jeep windshields and in helicopters; and rock and concrete that are used in underground bunkers As part of a program to develop advanced hydrocode design tools, we have implemented a brittle fracture model for glass into the SPHINX smooth particle hydrodynamics code W e have evaluated this model and the code by predicting data from onedimensional flyer plate impacts into glass, and data from tungsten rods impacting glass Since fractured glass properties, which are needed in the model, are not available, we did sensitivity studies of these properties, as well as sensitivity studies to determine the number of particles needed in the calculations The numerical results are in good agreement with the data INTRODUCTION The numerical prediction of ceramic, including glass and rocks, material strength, and fracture is important in the design of a number of military and commercial products The predictions are important in annor/anti-armor design, including the penetration and fracture of glass windshields; in the design of devices to defeat hardened, underground targets; in oil well recovery work in order to predict the fracture of rock; and in safety analyses for engines using ceramic blades where the effect of debris entering the engine needs to be predicted In the current work we use the SPHINX smooth particle hydrodynamics code (Stellingwerf'and Wingate, 1993; Wingate and Stellingwerf, 1994), described below, to predict data from one-dimensional experiments in which an aluminum flyer plate impacted a glass target (Raiser et al, 1994; Grady and Wise, 1993), and two-dimensional experiments in which a tungsten rod impacted glass, backed by mild steel (Anderson et al, 1

5 1993) In the flyer plate experiments, a VISAR (laser velocity interferometer system) was used to measure the velocity as a function of time at the rear of the glass plate In the two-dimensional experiments, a series of experiments was conducted, and the tip and tail positions of the tungsten rod were obtained as a function of time As has been noted previously (Mandell, 19931, the fracture model used for predictions of impacts into ceramics is critical In addition, a fracture model that is adequate to predict one-dimensionalexperiments may give very poor results when predicting multi-dimensional experiments In the current work we use the glass fracture model developed by Cagnoux (Cagnoux, 1985) and extended by Glenn and his co-workers (Glenn et al, 199) This model is described below SPHINX MODELS Smooth Particle Hydrodynamics (SPH) is a relatively new technique for doing hydrodynamics calculations It is a gridless, Lagrangian method in which fluid elements are represented by mass points that move according to the fluid equations of motion Each particle carries local values of density, temperature, pressure, and other fluid parameters Interpolation is used to find values of physical quantities between the particles The key feature of SPH is that it is gridless and thus does not have the mesh tangling problems of typical Lagrangian codes Since SPH is Lagrangian, it does not have the problems with advection that typical Eulerian codes have Also SPH only needs particles where the material is and thus does not have to zone up huge volumes of space The Los Alamos SPHINX code is the SPH code used in this work The current version of the code has many equations of state including perfect gas, Grueneissen, and SESAME (Holian, 1984) It runs in ld, 2D, 3D Cartesian coordinates, 2D cylindrically symmetric and 1D spherically symmetric (all in the same code) coordinate systems Elastic perfectly plastic, Johnson-Cook (Johnson and Cook, 1983) and Steinberg-Guinan (Steinberg et al, 198) strength of material models are in the code Two high explosive burn models are available Fracture modeling with SPHINX is an area of ongoing research Fracture models currently available include a simple void fracture model, a Grady-Kipp ( Grady and Kipp, 198) type model and most recently the Cagnoux-Glenn brittle fracture model, which was implemented for this project and used to predict the glass damage in the work discussed in this report The code has an option to solve the continuity equation independent of the normal SPH equations It uses Runge Kutta to do the time stepping The glass model developed by Cagnoux (Cagnoux, 1989, and extended by Glenn and his co-workers (Glenn et al, 199) was implemented into SPHINX This model consists of an ordinary differential equation for the 2

6 glass damage, and a prescription for the damaged glass strength properties and an equation of state The model is discussed below A scalar damage variable, D, is calculated from the following equation where Z is the maximum principal tensile stress, and B and b are material constants The damage is zero for intact glass and one for fully damaged glass Damage is accumulated only if Z is greater than a threshold value, ToThe values of B and b given by Cagnoux (Cagnoux, 1985) were used in the calculations shown in this report: B = 7 1-5kbar-seconds and b = 7 kbar-1 Once the damage is calculated, it is important to degrade the glass material strength and equation of state (EOS) in an appropriate manner A number of methods have been used, but in the Cagnoux-Glenn model, the bulk modulus, K; shear modulus, G; and yield strength, Y, are calculated as linear functions between the intact and fractured values f = fo ( 1 - D) + fo frd, where f is K, G, or Y The subscript o refers to intact glass properties and the subscript R refers to the ratio of the fractured glass property t o the intact glass property The EOS is dp dv =- Kv, where p is the pressure and v is the glass specific volume It should be noted that once damage starts to accumulate, the slope of the EOS equation, K, changes, resulting in increased glass pressure This provides the dilatation (bulking) seen in experiments A schematic of the glass EOS is shown in Fig 1The energy term added to the pressure EOS equation was not used in our work (Glenn et al, 199)This EOS was used for the glass in all of the calculations shown in this report 3

7 P 4 - ONSET OF DAMAGE HUGONIOT CURVE V Fig 1Intact and fractured glass pressure We varied the values of KR,YR,and GR until we matched one experiment, since the fractured glass properties have not been measured, to our knowledge We then used these values to predict other experiments The results of the sensitivity study done on the fractured glass properties are presented below SPHINX uses cgs units (grams, centimeters, seconds, and degrees Kelvin) Some constants in this report are given in kbar and microseconds because of their use in armor work ONE-DIMENSIONAL FLYER PLATES As indicated above, data from one-dimensional flyer plate experiments provide a necessary, but not sufficient, test of a brittle fracture model and of the implementation of the model into a hydrocode Four aluminosilicate glass flyer plate impact experiments were conducted at the Sandia National Laboratories (Raiser et al, 1994; Grady and Wise, 1993) In two experiments the 661-T6 aluminum flyer plates had a velocity of approximately 96 kdsec, and in the other two experiments the velocity was about 45 km/sec In each set of experiments, one experiment was conducted with a roughened glass surface and the other with a smooth surface Hydrocodes cannot predict the effect of the surface, so we predicted the experiments with smooth glass surfaces A schematic of the geometry is shown in Fig 2 4

8 El ALUMINIUM FLYER PLATE GLASS TARGET VELOCITY Figure 2 Schematic for the 1-DGlass Flyer Plate Predictions The experiment at the higher velocity apparently had a sfliciently large compressive strength that the glass spall strength, To, went to zero (Raiser et ai, 1994)For the two lower velocity experiments, spall strengths of 349and 335 kbar were reported (Grady and Wise, 1993)The SPHINX predictions therefore used a spall strength of zero for the higher velocity prediction and a spall strength of 34 kbar for the lower velocity one The aluminum flyer plate had a length of 36mm, and the glass target had a length of 5 mm An elastic plastic material strength model was used for each material The Grueneissen (Us-Up)equation of state (EOS) was used for the aluminum, and the Glenn EOS was used for the glass The aluminum properties used in the calculations are given in Table 1, the glass properties are given in Table 2, and a SPHINX sample input file is given in Appendix A 5

9 VARIABLE VALUE Density (gm/cm3) Sound Speed (cdmicrosecond) 538 EOS Slope 155 Shear Modulus (mar) 265 Yield Stress (Kbar) 275 Table T6 aluminum properties VARIABLE I VALUE I Density (gm/cm3) 26 Shear Modulus (Kbar) 333 Yield Stress (Kbar) 1 Bulk Modulus (Kbar) 417 YR (Ratio of fractured yield stress to 1 intact yield stress) GR (Ratio of fractured shear modulus 333 to intact shear modulus) KR (Ratio of fractured bulk modulus 333 I to intact bulk modulus) 1 I Table 2 Properties of aluminosilicate glass used in the SPHINX calculations I The SPHINX predictions of the glass free surface velocity for the two glass flyer plate experiments are shown in Figure 3 One thousand particles were used in these calculations, which are more than sufficient for a converged solution in one-dimension Calculations were also made with 1 and 2 particles for the lower velocity case The calculation with 1 particles was a little different from the one with 1 particles The calculations with 1 and 2 particles were virtually identical The elastic plastic material strength model was used for both materials 6

10 1 -- I " "! " "! ' " '! " "! " " ~ A s W 4 W > I - t 4 c K c e P II I --- 3k f&-j?* it ; *,, 1,,, 15, I i : L - 1, i, -,, 2 TIME (psec) I I iiuj : II i ii 5 -,I -- ih! i :- -DATA GLASS1 ---DATA GLASS3 SPALL STRENGTH, ---SPHINX ; SPHINX SPALL STRENGTH 34 KBAR ", - 1 i 1, 25,,, 1 3 Fig 3 Glass Free Surface Velocity It is seen from the above figure that the predictions are in reasonably good agreement with the data If the same spall strength is used for both experiments, either or 34 kbar, only one of the experiments can be predicted well TUNGSTEN RODS IMPACTING STEEL As a base case before doing the glass impact experiments, Anderson and his co-workers (Anderson et al, 1993) did experiments in which a tungsten rod impacted steel Since the main object of the present work is to evaluate brittle material strength and fracture models using the smooth particle hydrodynamics method, SPHINX predictions of data for impacts into metal were done to verify that the hydrocode input parameters and number of particles were correct These base case experiments consist of a blunt nosed tungsten alloy cylinder impacting armor steel as shown in Fig 4 The rod had a radius of 2 cm and a length of 5 cm The steel radius was 2 cm, and the length was 29 cm 7

11 TUNGSTEN ALLOY ROD ARMOR STEEL VELOCITY = 125 or 17 KM/SEC I Fig 4 Geometry for Tungsten Rod Impacting Steel Figure 5 shows the initial SPHINX geometry on the plane of symmetry, and Fig 6 shows the corresponding geometry at 6 microseconds In order to reduce the computer resources used, a variable SPH particle spacing was used, with a spacing of 11between adjacent particles This effect can be seen in Figures 5 and 6 where there is a fine zoning in the most important region of the problem near the axis of symmetry where it is needed and coarse zoning at the edges X Fig 5 SPHINX 2-D Axisymmetric Geometry for Tungsten Rod Penetrating Steel - Time = 8

12 4-2 2 X Fig 6 Penetration of a Tungsten Rod Into Steel - Time = 6 Microseconds 9

13 The computational model consisted of the elastic plastic strength model in the rod and the Johnson-Cook model (Johnson and Cook, 1983)in the steel No fracture model was used in these predictions The tungsten properties used in the calculations are given in Table 3, and the steel properties are given in Table 4 The Los Alamos SESAME tabular equations of state were used for both the tungsten and the steel (Holian, 1984) The SPHINX input file for run steel4 is given in Appendix B VARIABLE VALUE Density (g/cm3) Shear Modulus (Kbar) Yield Stress (Kbar) Table 3 Tungsten Properties IVARIABLE Iv A L m Table 4 Steel Properties Figure 7 shows the rod tip and tail positions as a function of time for the data and predictions of the tungsten rod penetrating into armor steel As can be seen, the SPHINX predictions are in good agreement with the data Predictions are shown for 37 and 128 SPH particles After 5 microseconds; only a small difference exists between the two predictions indicating that particle ("mesh")convergence has been achieved The quantities in parentheses in the figure legends are the computational run designations (eg steel4) 1

14 n DATA ROD NOSE DATA ROD TAIL -SPHINX ROD NOSE 37 PARTICLES (STEEL3) 7 : -----SPHINX ROD TAIL 37 PARTICLES (STEELO3) - _ SPHINX ROD NOSE 128 PARTICLES (STEEL4) SPHINX ROD TAIL 128 PARTICLES (STEEL4) > o & 1 8 1, TIME (psec) 5 6 Figure 7Rod Position - Tungsten Impacting Glass It is of interest to compare the computer times between runs with different numbers of particles All of the calculations done in this work were The CPU times used for the two steel runs are shown done on a Cray Y-MP in Table 5 INUMBER OF PARTICLES I CPU TIME (MINUTES) I Table 5Cray Y-MP CPU time used in the steel penetration calculations With this agreement for the penetration into a metal, the predictions into glass can be made knowing that discrepancies between the predictions and the data are due to the material strength and fracture model for the glass TUNGSTEN RODS IMPACTING GLASS The goal of this work is provide a hydrocode tool for use in annodantiarmor design, especially for design involving brittle material strength and fracture The materials of interest are ceramics, such as alumina and silicon carbide; and glass, which is used in truck and jeep windshields, and in helicopters A brittle material strength and fracture model can only be qualified for design if it can predict multi-dimensional problems Therefore, as part of this qualification effort, we predicted two-dimensionalimpact 11

15 experiments into soda lime glass (Anderson et al, 1993) Figure 8 shows a schematic of the geometry, which consists of a tungsten alloy rod impacting glass, backed by mild steel TUNGSTEN ALLOY WINDOW GLASS MILD STEEL L VELOCITY = 125 or 17 KM/SEC Fig 8 Geometry for Tungsten Rod Impacting Glass The dimensions and properties used for the tungsten, glass, and mild steel for these calculations are shown in Tables 5-7 The input file for run g5 is given in Appendix C The Grueneissen EOS and the elastic plastic strength model were used for the tungsten and mild steel In these calculations, only the glass was allowed to fracture Table 5Tungsten rod dimensions and properties for the glass impacts VARIABLE VALUE in n Intact shear modulus (kbar) 333 Intact bulk modulus (kbar) Damage threshold, Zo (kbar) Table 6 Glass dimensions and properties for the glass impacts Diameter (cm) Length (cm) Density (gm/cm3) 12

16 1 I VALUE VARIABLE Diameter (cm) 15 Length (cm) 1 Density (gm/cm3) 785 Shear modulus (kbar) Yield stress (kbar) Sound Sr>eed( d u s e c ) 596 EOS slope, S Table 7 Mild steel dimensions and properties for the glass impacts Figures 9 and 1 show the SPHINX plane of symmetry geometry at time zero A variable particle spacing of 11was again used, as can be seen in the figures Figure 11shows the mesh at 325 microseconds The tungsten rod is almost completely eroded by this time The glass model used in this work, the Cagnoux-Glenn model, requires a knowledge of both the intact and the fractured glass properties - bulk modulus, K, shear modulus, G; and yield stress, Y Intact glass properties are reasonably well known, but the properties of the fractured glass are not available Therefore we have varied the ratios of the fi-actured to the intact properties, KR, GR, and YR, t o match the experiments in which the rod velocity was 125 W s e c We then ran the higher velocity experiment, which was at 17 kdsec, t o determine if the fractured glass properties were valid for conditions other than those for which they were determined 3 2 x io 1 2 X Fig 9 Initial SPHINX Geometry for a Tungsten Rod Impacting Glass - Time = 13

17 X Fig 1 Initial Geometry for a Tungsten Rod Impacting Glass Showing Individual SPH Particles - Time = 7 T -7 h x Fig 11Final Geometry for a Tungsten Rod Penetrating Glass Time = 325 Microseconds 14

18 Figure 12 shows the tungsten rod nose position for the experiments in which the rod was at an initial velocity of 125 kdsec This figure shows the data, a calculation without damage, and a series of calculations with damage in which the ratio of the fractured yield stress to the intact yield stress was varied (YR) For Yr = 1, only the bulk modulus and shear modulus are decreased after the glass is fractured Several conclusions can be reached from these results Numerical predictions of glass impacts are greatly in error when no fracture of the glass is allowed In addition many models let the glass strength go to zero once a cell completely fractures ( D = 1 ) The model used in this work shows that some glass strength remains after fracture The results are sensitive to the value of YR, but in all cases the predictions are much better using any nonzero value of YR than assuming that no fracture occurs 2 n E TIME (psec) Fig 12 Predictions of Tungsten Rods Penetrating Glass - Effect of Fractured Glass Yield Stress Figure 13 shows the effect of the number of SPH particles used in the calculation A balance should be achieved between having enough particles so that the answers are converged and not wasting computer resources by using too many particles A nominal number of particles is input t o SPHINX, but an internal algorithm determines the actual number of particles used The figure shows that 84 particles is insufficient, but the results for 1392 and 15

19 2286 particles are very close Unless otherwise noted, the calculations shown in this report were done using 1392 SPH particles TIME (psec) 25 3 Fig 13Predictions of Tungsten Rods Penetrating Glass at 125 Km/Sec Effect of the Number of Particles Figure 14 shows the results of varying the fractured glass shear modulus The figure shows that varying the ratio of the fractured glass shear modulus t o the intact value, GR, over a wide range had a relatively small effect on the rod tip position results A value of 333was used for GR in the majority of the calculations 16

20 I T 1 4 6= ~ K - : DATA ROD NOSE 8 R = 333 G5) SPHINX 1 - R = 1 - GR = 1 15 G73 2 TIME (Fsec) 25 3 Fig 14 Predictions of Tungsten Rods Penetrating Glass at 125 Km/Sec Effect of Fractured Glass Shear Modulus The predicted results for different fractured glass bulk modulii are shown in Figure 15 The results do not vary smoothly as the value of KR is changed This effect may be due to the nonlinear interactions between the damage, KR, and the pressure As damage, D, increases, the bulk modulus changes, resulting in a higher pressure, which results in further damage In addition, the fractured glass properties are not constants, as used in this work, but functions of the pressure, as well as other variables 17

21 w v) 6 Z n K TIME (psec) Fig 15 Predictions of Tungsten Rods Penetating Glass at 125 W S e c Effect of Fractured Glass Bulk Modulus Figure 16 shows both the rod tip and tail positions for the calculation that best matched the data, for a rod initial velocity of 125 k d s e c As can be seen, the agreement between the predictions and the data is good 18

22 TIME (psec) Fig 16 Predictions of Tungsten Rods Penetrating Glass at 125 Km/Sec Using the values of the fractured glass properties determined for the experiments in which the rod velocity was 125 kdsec, the experiments in which the rod velocity was 17 kdsec were predicted These results are shown in Figure 17 The comparison between the data and the SPHINX predictions is very good 19

23 2 E n 15 2 = 2 t 1 v) a n 5 U TIME (psec) 2 25 Fig 17 Predictions of Tungsten Rods Penetrating Glass at 17 Km/Sec Table 8 shows the Cray Y-MP CPU times required for the calculations using three different numbers of SPH particles The SPHINX algorithm calculates the number of particles t o be used, based on the requested number of particles Clearly the least number of particles that will result in a converged solution should be used in order to minimize the computer resources required RUN NO NO PARTICLES USED CPU TIME (MINUTES) G G G Table 8 CPU Times For SPHINX Predictions of Tungsten Rods Penetrating Glass at 125 W s e c CONCLUSIONS The Cagnoux-Glenn (Cagnoux, 1985; Glenn et al, 199) glass fracture model has been implemented into the SPHINX smooth particle 2

24 hydrodynamics code The model has been evaluated by predicting two different types of experiments In the first set of experiments, which are one-dimensional, an aluminum flyer plate impacted aluminosilicate glass The free surface velocities predicted by SPHINX match the data if different spall strengths are used for the higher and lower velocity experiments Two-dimensional experiments in which a tungsten rod impacts soda lime (window) glass were also predicted The results again match the data well, considering that the fr-actured glass properties are unknown and had to be estimated The fractured glass properties estimated for one experiment were used in the predictions of the other experiments and the data and predictions agree reasonably well Even though the global experimental results predicted by SPHINX, using the Cagnox-Glenn model, are in good agreement with the data, some armor/anti-armor problems and oil well hydrofracturing predictions, require the predictions of more fracture details then can be obtained from the Cagnoux-Glenn model These problems require the predictions of the actual crack postions and lengths, and in some cases, more exact initial crack times In order to make these more detailed predictions, we are implementing more advanced brittle fracture models into SPHINX ACKNOWLEDGMENT This work was supported by the DOE/DoD Munitions Technology Development Program We would like to thank Dr L Schwalbe, Project Leader, and Dr J Repa, Program Manager, for their support of this work We would also like to thank Dr James D Walker and Dr Charles E Anderson, Jr, Southwest Research Institute, for providing digitized rod tip and tail position data, and for answering a number of questions about their work 21

25 REFERENCES Charles E Anderson, Jr, Volker Hohler, James D Walker, and Alois J Stilp, Penetration of Long Rods into Steel and Glass Targets: Experiments and Computations, Ballistics '93, 14th International Symposium, Quebec, Canada, September 26-29, 1993 J Cagnoux, Modele Phenomenlogique D'Ecaillage D'Un Pyrex (PhenomenologicalModel of Spalling of Pyrex Glass), Journal De Physique, Colloque C5,supplement au no8 Tome 46,1985 L A Glenn, B Moran, and A Kusubov, Modeling Jet Penetration In Glass, Conference on the Application of 3-D Hydrocodes to Armor/Anti-Armor Problems, Ballistic Research Laboratory, Aberdeen Proving Grounds, MD, May 199 D E Grady and M E Kipp, Continuum Modelling of Explosive Fracture in Oil Shale, Int J Rock Mech Min Sci & Geomech Abstr, Vol 17, pp ,198 D E Grady and J L Wise, Dynamic Properties of Ceramic Materials, Sandia National Laboratories Report SAND93-61, September, 1993 K S Holian, T-4 Handbook of Material Properties Data Bases, Los Alamos National Laboratory Report LA- 116-MS,November, 1984 G R Johnson and W H Cook, A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures, Seventh International Symposium on Ballistics, The Hague, The Netherlands, 1983 David A Mandell, Prediction of Alumina Penetration, Los Alamos National Laboratory Report LA- 1252, February, 1993 G F Raizer, J L Wise, R J Clifton, D E, Grady, and D E Cox, Plate Impact Response of Ceramics and Glass, J Appl Phys, 75 (8), April 15,1994 D J Steinberg, S G Cochran, and M W Guinan, A Constitutive Model for Metals Applicable at High Strain Rates, J Appl Phy, 51 (3), pp , 198) R F Stellingwerf and C A Wingate, Impact Modeling With Smooth Particle Hydrodynamics, Int J Impact Engng, Vol 14, pp , 1993 CA Wingate and R F Stellingwerf, Los Alamos SPHINX Manual Version 57, Los Alamos National Laboratory Report LAUR , January 28,

26 APPENDIX A - SPHINX INPUT FOR ONE-DIMENSIONAL FLYER PLATE CALCULATIONS cat wg24 # AL FLYER PLATE IMPACTING GLASS TARGET AT 45 METERSBEC # Titles; problem-title WISE GLASS; run-title WG24 # Damage; damage TRUE print-damage-tables TRUE Damagedtmin 5 # Anything > 1 turns off damage dt control # Density; continuity TRUE # Dumps; restart-time-skip-fraction history-time-skip-fraction 1 #Exit; max-steps ; max-time 3e-6 # Geometry; cylindrical FALSE; dimension 1 # Global; step-print-delta 1 # Graphics; graphics FALSE; particleglot-cycle-frequency 5 plot-xminmax 1-44; plotyminmax 1-62 # Particles; nparticles 1 # Strength; strength TRUE; disable-me1 t-cutoff TRUE dump-strength-values FALSE; print-strength-tables FALSE # H; h-vary FALSE; h-inp 1 Lagrangian-probe 1 dt-mult 2 h-inp 15 #############FLYER############################### # Set up the projectile create-object rod density ; velocity 45e+5 type cylinder radius 25 length 36 strength-material a1-661-t6; strength-model Basic eos-material a1-66 l-t6; eos-model Grueneissen end-objec t translate-object rod -18 ############# Plate################################# # Set up the plate create-object plate density 26 type cylinder radius 25 length 5 strength-material glass; strength-model Basic 23

27 eos-materid glass; eos-model Glenn damage-material glass; damage-model Cagnoux-Glenn end-object translate-object plate 25 ######### Strength and EOS Tables materi al-s trength glass shear-modulus 333e12 yield-limit 1e9 Tcutoff 5 material-damage glass Cagnoux-Glenn B 7 Cagnoux-Glenn b -7e-12 Cagnoux-Glenn tau 34e9 Cagnoux-Glenn Yratio 1 Cagnoux-Glenn Gratio,333 Cagnoux-Glenn Kratio 333 grun-m aterial rho- 26 csq- 222el1 cv- 44e6 a-mol a-atm z-atm 26 ion-en 783 gamma-g 1 s-shock 1 gamma-mol cv-liq 44e6 189 tmelt belt 247e9 tvap 3135 hvap 626el tdiss hdiss tcp 65 pmin -34e9 dbar sbar glass glenn-material glass 24

28 rho- 26 cv- 44e6 pmin K -34e9 417e12 25

29 - APPENDIX B SPHINX INPUT FOR TUNGSTEN RODS IMPACTING STEEL CALCULATIONS cat steel4 # KE ROD IMPACTING ARMOR STEEL # Titles; problem-title KE ROD - STEEL; run-title STEEL4 # Density; continuity TRUE # Dumps; restart-time-skip-fraction 1 history-time-skip-fraction 5 #Exit; max-steps ; max-time 6e-6 # Geometry; cylindrical TRUE; dimension 2 # Global; step-print-delta 1 # Graphics; graphics FALSE; particle-plot-cycle-frequency 2 plot-xminmax 1 8; plotyminmax # Particles; nparticles 5 nparticle-mult 1 # Strength; strength TRUE; disable-melt-cutoff FALSE dump-strength-values TRUE; print-strength-tables TRUE # H; h-vary TRUE; h-inp 1 use_grid_gen TRUE dt-mult 8 disable-av-dt-control TRUE sph-form 23 ############# Rod########################### # Set up the projectile create-object rod density 1775; velocity 125e+5 type cylinder radius 2 length 5 move-to-h rod y 5 strength-material W-Libersky; strength-model Basic material-strength W-Libersky shear-modulus 1388e12 yield-limit 13e9 Tcutoff 5 eos-material W1; eos-model sesame sesame-material-number 354 1; sesamegmin -2e12 w1 grun-material rho csq- 1594e1 cv- 13e6 184 a-mol 26

30 a-atm z-atm ion-en gamxna-g 154 s-shock 1237 gamma-mol cv-liq 13e6 tmelt 368 hmelt O191eIO tvap 593 hvap 435e1 tdiss hdiss t CP 15 pmin -6e9 dbar sbar e e12 end-object translate-object rod -25 ####### STEEL############################## # Set up the plate create-object bplate density 781 type cylinder radius 2 length 29 npmult 2 move-to-h bplate y 5 Ratr 11 strength-material armor-steel; strength-model Johnson-Cook eos-material fe; eos-model sesame sesame-material-number 2 145; sesame-pmin -2e12 end-objec t translate-object bplate

31 - APPENDIX C SPHINX INPUTFOR TUNGSTEN RODS IMPACTING GLASS CALCULATIONS #debug-eos-glenn TRUE #debug-flow TRUE #debug-eos TRUE # KE ROD IMPACTING GLASS # Titles; problem-title KE ROD - GLASS; run-title g5 glass-or = 75 rratio = 11 # Damage; damage TRUE print-damage-tables TRUE Damagedtmin 5 # Anything > 1turns off damage dt control ## Density; continuity TRUE # Dumps; restart-time-skip-fraction history-time-skip-fraction 5 #Exit; max-steps ; max-time 325e-6 # Geometry; cylindrical TRUE; dimension 2 # Global; step-print-delta 1 particleglo t-cycle-frequency 1 ## Graphics; graphics FALSE; plot-xminmax ; plotyminmax # Particles; nparticles 5 nparticle-mult 1 use_grid_gen TRUE dt-mult 8 # Strength; strength TRUE; disable-me1 t-cutoff FALSE dump-strength-values FALSE; print-strength-tables TRUE # H; h-vary TRUE; h-inp 1 # new energy eq; sph-form 23 ############# Rod############################# # Set up the projectile create-object rod density 1775; velocity 125e+5 type cylinder radius 29 length 725 npmult 2 #move-to-h rod y 5 strength-material W-Libersky; strength-model Basic eos-material W1; eos-model Grueneissen end-object translate-object rod -4 28

32 create-object bplate density 785 type cylinder radius glass-or length 1 #move-to-h bplate y 5 Ratr rratio strength-material mild-steel; strength-model Basic eos-material fe; eos-model Grueneissen end-object translate-object bplate 25 ####### GLASS # Set up the plate create-object glass #move-to-h glass y 5 density 25 type cylinder radius glass-or length 2 Ratr rratio strength-material glass; strength-model Basic eos-material glass; eos-model Glenn damage-material glass; damage-model Cagnoux-Glenn end-object translate-object glass 1 ######### Strength and EOS Tables material-strength W-Libersky shear-modulus 1388e 12 yield-limit 13e9 Tcutoff 5 material-strength glass shear-modulus 333e12 yield-limit 1e9 Tcutoff 5 material-damage glass Cagnoux-Glenn B 7 Cagnoux-Glenn b -7e-12 Cagnoux-Glenn tau 9e9 Cagnoux-Glenn Yratio 8 Cagnoux-Glenn Gratio 333 Cagnoux-Glenn Kratio 333 grun-mat erial rho w1 29

33 csq- 1594elO cv- 13e6 a-mol 184 a-atm z-atm 74 ion-en 918 gamma-g 154 s-shock 1237 gamma-mol cv-liq 13e6 tmelt 368 hmelt 191e1 tvap 593 hvap 435e1 tdiss hdiss tcp pmin dbar sbar 15-6e e e12 grun-mat erial rho- 25 csq- 222e1l cv- 44e6 a-mol a-atm z-atm 26 ion-en 783 gamma-g 1 s-shock 1 gamma-mol cv-liq 44e6 tmelt 189 hmelt 247e9 tvap 3135 hvap 626e1 tdiss, hdiss tcp 65 pmin -9e9 dbar sbar glass glenn-material glass 3

34 rho- 25 w- 44e6 pmin -9e9 K 555e12 31